Presumably you don't actually have £2k surplus each month (as in "left in your bank account at the end of the month and transferred to a savings account" or similar) because if you did you would have enough for the car outright unless you had had other significant expenditure.
So presumably you have £2k after housing costs, utility type bills and groceries, but not leisure, entertaining, clothing, enjoyment type costs?
The ONLY way to work out where the money is going is to track it for at least a month.
Do you mainly spend cash? How much cash are you getting out a week? What are you spending this on.
If you mainly spend on cards it is much easier as you can go and look at the last 3 months of statements.
eg: I probably don't spend near to £50 cash month as I put everything on my Tesco credit card for the points - I put £1.17 on it today as I popped into tesco for something and as it's the clubcard as well it's easier to just pay with it. So for me tracking what I spend is easy - look at the credit card statement.
If you want to save then set up a standing order, probably into an ISA or a regular saver account, that goes out just after you get paid - that way you don't really see the money in your account and so don't figure it in your spending.
Personally, if I could see where my money was going, knew that I could easily cut down to meet the payments, could put £5k towards the new car as you suggest and could get an interest free deal to pay off the remainder over maybe 12-24 months then I would consider it.
Otherwise, and in you case as you don't know where your money is going, as you think you have £2k discretionary income a month, I'd look to be saving £500 - £1k a month and buy the car in 6-12 months time.